Reduce to lowest terms: $ \dfrac{5}{4} \div - \dfrac{6}{7} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{6}{7}$ is $- \dfrac{7}{6}$ Therefore: $ \dfrac{5}{4} \div - \dfrac{6}{7} = \dfrac{5}{4} \times - \dfrac{7}{6} $ $ \phantom{ \dfrac{5}{4} \times - \dfrac{7}{6}} = \dfrac{5 \times -7}{4 \times 6} $ $ \phantom{ \dfrac{5}{4} \times - \dfrac{7}{6}} = \dfrac{-35}{24} $